Psychrometry/Hygrometry
Humidification operations
(Air-water-contact operations)
Psychrometry is the subject which deals with determination of the
properties of gas-vapor mixtures. The air-water vapor system is by far
the one most commonly encountered.
The system of air and water is important, not only with regard to air
conditioning for physiological comfort, but also with regard to water
cooling and drying.
In many of the unit operations it is necessary to make calculations
involving the properties of mixtures of air and water vapor. Such
calculations may require a knowledge of the amount of water vapor
carried by air under various conditions, of the enthalpy of mixtures of
air and water vapor, of the volume of air-water mixtures, and of the
change in enthalpy, water content, and temperature when water is
is brought into contact with air.
Also, there are frequent opportunities to apply psychrometric
principles to other systems in connection with problems of solvent
recovery and the removal of organic vapors.
Examples of this are in the dry-cleaning industry where recovery of the
Stoddard’s solvent, carbon tetrachlorides, and other valuable materials
is essential for economical operation.
Again there are cases where it is desired to recover organic vapors but
at the same time to prevent air from coming in contact with these
vapors because of the explosion and fire hazard. In such cases the
carrier gas may be nitrogen or a flue gas, instead of air. All these
operations are concerned with vapor-carrying capacity of the carrier
gas and with the engineering variables which affect this capacity.
Humidification and dehumidification involve the transfer of material
between a pure liquid and a fixed gas which is insoluble in the liquid.
In these operations, both heat transfer and mass transfer occur
simultaneously and influence one another.
In humidification operations, especially as applied to the air-water
system, a number of rather special definitions are in common use. The
usual basis for engineering calculations is a unit mass of vapor-free
gas, where “vapor” means the gaseous form of the component which is
present only in gaseous form. In this discussion a basis of 1 Ib of
vapor-free gas is used . In the gas phase the vapor will be referred to
as component A and the fixed gas as component B. Because the
properties of a gas-vapor mixture vary with total pressure, the pressure
must be fixed. Unless otherwise specified, a total pressure 1
atmosphere (atm) is assumed. Also, it is assumed that mixtures of gas
and vapor follow the ideal-gas laws.
Humidity (H, also called Humidity ratio or absolute humidity):
Mass of vapor carried by unit mass of vapor-free gas, i.e., pounds of
vapor carried by 1 pound of vapor-free gas. For air-water system, H is
the pounds of water vapor carried by 1 Ib of dry air. So defined,
humidity depends only on the partial pressure of the vapor in the
mixture when the total pressure is fixed . If the partial pressure of the
water vapor
is atm, then as we know, molal ratio of water vapor
to dry air at 1 atm is equal to the ratio of partial pressures.
--------------------------(1)
Again,
Again,
--------------------------(2)
Relative Humidity or Percentage Relative Humidity, HR
When a volume of air at a given temperature holds the maximum
amount of water vapor, the air is said to be saturated. Hence relative
humidity which is a dimensionless quantity corresponds to the watervapor content of the air relative to its maximum content at saturation at
the same dry bulb temperature.
Relative humidity can also be defined as the ratio of the mole fraction
of the water vapor in a given moist air sample to the mole fraction of
water vapor in an air sample of saturated moist air at the same
temperature and pressure.
It can be defined as ratio of the partial pressure of water vapor to the
vapor pressure of the liquid at the gas temperature.
It is usually expressed on a percentage basis, 100 per cent humidity
means saturated gas and 0 per cent humidity means vapor-free gas.
--------------------------(3)
What does it mean if the relative humidity of air is 25 percent?
That represents the amount of moisture in the air. That means that the
air is currently holding 25% of the maximum possible amount of
moisture that it can hold.
What does it mean if the relative humidity of air is 50 percent?
That means that the air is currently holding 50% of the maximum
possible amount of moisture that it can hold.
Let's say that a certain parcel of air can hold 30 grams of water vapor
per cubic meter of air, but it only has 15 grams of water vapor per
cubic meter of air.
The air masses above the tropical deserts such as the Sahara (Africa)
and Mexican (Central America) deserts contain vast quantities of
moisture as invisible water vapor; because of the high temperatures,
however, relative humidities are very low. Conversely, air in very high
latitudes, because of low temperatures, is frequently saturated even
though the absolute amount of moisture in the air is low.
Percentage Saturation or Percentage Humidity, HA
The ratio of humidity (H) to the saturation humidity (Hs) is defined as
the percentage humidity (HA).
----------------------------------(4)
Saturated gas is gas in which the vapor is in equilibrium with the liquid
at the gas temperature. By Dalton’s law, the partial pressure of water
vapor in the saturated gas equals the vapor pressure of the liquid at the
gas temperature. If Hs is the saturation humidity and pA the vapor
pressure of the liquid,
----------------------------------(5)
Substitution of H from equation (1) and Hs from equation (5) into in
equation (4) gives
-------------(6)
Now except at 0% or 100% humidity (that means at unsaturation),
the partial pressure is less than vapor pressure of water at the given
temperature then the term
hence
Therefore,
is bigger than the term
Percent humidity is less than relative humidity.
Dew Point or Saturation Temperature
Dew point is the temperature to which a mixture of air and water vapor
is be cooled in order to become saturated. It is also known as saturation
temperature and is at the temperature at which a given mixture of
water vapor and air is saturated, i.e. The temperature at which water
exerts a vapor pressure equal to the partial pressure of water vapor
in the given mixture.
At a given temperature and humidity, moist air contains some moisture
depending upon the humidity. Suppose, if this air is cooled, as the
temperature decreases the relative humidity increases, and a stage
comes where the partial pressure of moisture in the air becomes equal
to the vapor pressure of the water at that temperature. In a way we can
say that the air gets fully saturated with the moisture. Any further
decrease in temperature, results in the condensation of moisture from
the air. Thus, dew point is defined as the temperature at which mist or
dew starts forming. Because dew starts forming on the clean and shiny
surfaces, it is known as dew point.
As an example, suppose the air in a room at 700F is at 50% relative
humidity.
From steam tables, the vapor pressure of water at 700F is 0.3631 psi,
which means that the air at 50% humidity holds water vapor with a
partial pressure of (0.50) (0.3631) or 0.1812 psi.
If the temperature is dropped to the point where 0.1812 psi equals the
water vapor pressure (around 520F), the air becomes saturated with
water and any further drop in temperature will cause condensation. The
dew point of this air mixture is then 520F. Obviously, if the air were
already saturated at 700F (i.e., 100% relative humidity), the dew point
would also be 700F.
Problem 1:
The partial pressure of water vapor in a storage area, maintained at a
temperature of 250C and a pressure of 101.3 kPa, is 2 kPa. Calculate
the relative humidity and percentage saturation. At 250C the pure
component vapor pressure of water is 3.166 kPa.
From the definition of relative humidity equation (3)
From the definition of percentage saturation:
There is a significant
difference
between
relative humidity and
percent saturation for a
given mixture of water
vapor and air
Enthalpy of Moist Air, Hy
Enthalpy is a thermodynamic term used to define the amount of energy
contained in a dry air/water vapor mixture. The energy contained in
the mixture can be present both as a sensible heat (indicated by dry
bulb temperature) and latent heat of vaporization (energy content of
the water vapor).
Total enthalpy (Hy) is the enthalpy of 1 Ib of gas (dry air) plus
whatever vapor it may contain.
To calculate Hy two reference states must be chosen, one for gas
(component B) and one for vapor (component A). Let T0 be the datum
temperature chosen for both components and base the enthalpy of the
water (component A) on liquid water at T0.
Let the temperature of the gas be T and the humidity H. The total
enthalpy is the sum of three items:
Sensible heat of water vapor
Latent heat of the liquid at T0
Sensible heat of the vapor-free gas (dry air)
-------------(7)
Humid Heat or Specific Heat, Cs
It is defined as the quantity of heat required to raise the temperature of
1 Ib of dry air plus whatever vapor it may contain, by 10F. Thus
-------------(8)
Equation (7) can be rearranged as follows:
-------------(9)
Humid Volume or Specific Volume, vH
Volume occupied by one kg of dry air along with the associated
moisture vapor at a given humidity and temperature.
It is calculated using ideal gas law for the volumes of 1 kg of dry air
and associated moisture vapor. Thus the specific volume is the
summation of
Volume occupied by 1 kg of dry air at temperature T
Volume occupied by the water vapor associated with the dry air at
temperature T and humidity H
1 Kg mole or 29 Kg air at 00C or 273 K occupies 22.4 m3
1 Kg air at T K occupies
m3
In which 29 is the molecular weight of air and T is the degree
centigrade.
1 Kg mole or 18 Kg vapor (H2O) at 00C or 273 K occupies 22.4 m3
1 Kg vapor (H2O) at 1K occupies =
m3
H Kg Vapor (H2O) at TK occupies
So by definition
m3
Humid volume, vH
-------------(a)
Where T is the temperature in Kelvin. For dry air H=0 and vH is the
specific volume of dry air. For saturated air, HA=100, H=Hs, and vH
becomes the saturated volume.
Adiabatic Saturation Temperature
Adiabatic saturation temperature of moist air is the temperature that air
reaches when it is saturated adiabatically.
We know that at wet-bulb temperature, neither the humidity nor
the temperature of the gas is appreciably changed.
If the gas is passed over the liquid at such a rate that the time of
contact is sufficient for equilibrium to be established between the gas
stream and the liquid, the gas will become saturated and both phases
will be brought to the same temperature.
 In a thermally insulated system, the total sensible heat falls by an
amount equal to the latent heat of the liquid evaporated.
As a result of continued passage of the gas, the temperature of the
liquid gradually approaches an equilibrium value which is known as
the adiabatic saturation temperature.
These conditions are achieved in a tall thermally insulated
humidification column through which gas of a given initial
temperature and humidity flows counter-currently to the liquid under
conditions where the gas is completely saturated at the top of column.
On the other hand, if the apparatus is smaller and the time and
intimacy of contact less, the air will discharged at a humidity less than
saturation and at a temperature somewhat higher than that of the
circulating water.
If the liquid is continuously circulated round the column, and if any
fresh liquid which is added is at the same temperature as the
circulating liquid, the temperature of the liquid at the top and bottom
of the column, and temperature of the gas at the top, approach the
adiabatic saturation temperature.
Temperature and humidity differences are a maximum at the bottom
and zero at the top, and therefore the rates of transfer of heat and mass
decrease progressively from the bottom to the top of the tower. This is
illustrated in the Figure.
From a heat balance over the column it is seen that the heat of
vaporization of the liquid must come from the sensible heat in the gas.
The temperature of the gas falls from T to the adiabatic saturation
temperature Ts and its humidity increases from H to Hs (the saturation
value at Ts). For unit mass of dry gas:
-------------(10)
Where Cs is the humid heat of gas and
s
the latent heat of
vaporization at Ts. Cs is almost constant for small changes in H.
For any given value of Ts,
The equation (10) contains :variables only H and T
The equation is, therefore, the equation of a curve (called adiabatic
cooling line) on the humidity chart.
If a value assumed for Ts (thus fixing
s
and Hs), equation (10) can
be plotted on the humidity chart, and this curve will intersect the 100%
line at the Ts, Hs.
Each adiabatic cooling line represents the composition of all gases
whose adiabatic saturation temperature is given by its point of
intersection with the 100 per cent relative humidity curve.
For the air-water system, the adiabatic cooling lines enable the change
in composition of a gas to be followed as it is humidified by contact
with water at the adiabatic saturation temperature of the gas.
Wet Bulb Temperature
Wet bulb temperature is the steady state nonequilibrium temperature
reached by a small mass of liquid immersed under adiabatic conditions
in a continuous stream of air. The mass of liquid is so small in
comparison with the gas phase that there is only a negligible change in
the properties of the gas, and the effect of the process is confined to the
liquid. The method of measuring the wet-bulb temperature is shown in
the figure.
A thermometer, or an equivalent temperature-measuring device such as
a thermocouple, is covered by a wick, which is saturated with pure
liquid and immersed in a stream of gas having a definite temperature T
and humidity H. Assume that initially the temperature of the liquid is
about that of the gas. Since the gas is not saturated, liquid evaporates,
and because the process is adiabatic, the latent heat is supplied at first
by cooling the liquid. As the temperature of the liquid decreases below
that of the gas, sensible heat is transferred to the liquid (from the gas).
Ultimately a steady state is reached at such a liquid temperature that
the lost of heat from the water by evaporation is exactly blanced by
the heat passing from the air into the water as sensible heat. It is this
steady-sate temperature, denoted by Tw, that is called the wet-bulb
temperature. It is a function of both T and H.
To measure the wet-bulb temperature with precision, three precautions
are necessary: The wick must be completely wet so no dry areas of the
wick are in contact with the gas; the velocity of the gas should be large
enough to ensure that the rate of heat flow by radiation from warmer
surroundings to the wet bulb is negligible in comparison with the rate
of sensible heat flow by conduction and convection from the gas to the
bulb and ; if the makeup liquid is supplied to the wet bulb, it should be
at the wet-bulb temperature. When these precautions are taken, the
wet-bulb temperature is independent of gas velocity over a wide range
of flow rates.
The wet bulb temperature apparently resembles the adiabatic saturation
temperature Ts. Indeed, for air-water mixtures the two temperatures are
nearly equal. However, this is accidental and does not apply to
mixtures of substances other than air and water.
The wet bulb temperature differs fundamentally from the adiabaticsaturation temperature.
In the latter the temperature and humidity of the gas vary during
process, and the end point is a true equilibrium, rather than a dynamic
steady state.
Commonly, an uncovered thermometer is used along with the wet bulb
to measure T, the actual gas temperature, and the gas temperature is
usually called the dry-bulb temperature.
Theory of wet-bulb temperature
At the wet-bulb temperature the rate of heat transfer from the gas to
the liquid may be equated to the product of the rate of vaporization and
the sum of the latent heat of evaporation and the sensible heat of the
vapor. Since the radiation may be neglected, the balance may be
written as:
-------------(11)
Where q = rate of sensible heat transfer to the liquid
NA = the molal rate of vaporization
λw= latent heat of the liquid at the wet-bulb temperature Tw
The rate of heat transfer may be expressed in terms of the area
Rate of heat transfer may be expressed in terms of the area, the
temperature drop, and the heat-transfer coefficient in the usual way, or
-------------(12)
The rate of mass transfer may be expressed in terms of the mass
transfer coefficient, the area, and the driving force in mole fraction of
vapor, or
-------------(13)
If the wick is completely wet and no dry spots show, the entire area of
the wick is available for both heat and mass transfer, and the areas (A)
in equations 12 and 13 are equal.
Since the temperature of the water is constant, no temperature
gradients are necessary in the liquid to act as driving forces for heat
transfer within the water, the surface of the liquid is at the same
temperature as the interior, and the surface temperature of the water Ti
equals to Tw. Since the water is pure, no concentration gradients exists,
and granting interfacial equilibrium, xi is the mole fraction of water
vapor in saturated air at temperature Tw. It is convenient to replace the
mole fraction terms (xi and x) in equation 13 by humidities. By the
definition of humidity using equation 2:
-------------(14)
Where Hw is the saturation humidity at the wet-bulb temperature.
Substitution of q from equation 12 and NA from equation 13 into
equation 11 gives:
-------------(15)
Equation 15 may be simplified without introducing serious error in
the usual range of temperatures and humidities as follows: 1. the
relative velocity factor φ is nearly unity and can be omitted, 2. the
sensible heat term CpA (T─Tw) is small in comparison with λw
and can be neglected, 3. the terms Hw/18 and H/18 are small in
comparison with 1/29 and may be dropped from the denominators of
the humidity terms. With these simplifications equation 15 becomes
-------------(16)
For a given wet-bulb temperature, both λw and Hw are fixed obtained
from the humidity chart. The relation between H and T then depends
on the ratio of hy/ky.
Heat transfer by conduction and convection between a stream of fluid
and a solid or liquid boundary depend on Reynolds number DG/µ and
the Prandtl number Cpµ/k
Where D = Diameter of the tube, G = Mass velocity = vρ
µ = Viscosity of liquid
The mass transfer coefficient depends on the Reynolds number and the
Schmidt number µ/ρDv . For turbulent flow of the gas stream heat
and mass transfer coefficients can be expressed as
-------------(16.a)
-------------(16.b)
Where b, n, m are constants
= Average molecular weight of gas stream
Substitution of hy from equation (16.a) and ky from equation (16.b) in
equation (16), assuming
= MB gives
-------------(16.c)
And
-------------(16.d)
The experimental value of hy/MBky for (when m = 2/3)
Water------------------------0.26
Benzene-------------------- 0.41
Carbon tetrachloride------0.44
Chlorobenzene----------- 0.44
Ethyl acetate----------------0.42
Toluene----------------------0.44
The value of hy/MBky can also be calculated from the following
relation:
Humidity chart and its construction
A convenient diagram showing the properties of mixtures of a
permanent gas and a condensable vapor is the humidity chart. A chart
for mixtures of air and water at 1 atm is shown in the figure. Many
forms of such charts have been proposed. The figure is based on the
Grosvenor chart.
On the figure temperatures are plotted as x -coordinate and humidities
as y-coordinate.
Any point on the chart represents a definite mixture of air and water.
The curved line marked “100%” gives the humidity of saturated air as
a function of air temperature.
By using the vapor pressure of water the coordinates of points on this
line are found by use of equation 5 as follows:
Any point above and to the left of the saturation line represents a
mixture of saturated air and liquid water- mixtures of air and water
vapor represented by the points (above and to the left of the saturation
line) cannot ordinarily exist. This region is important only in checking
fog formation.
Any point below the saturation line represents under-saturated air, and
a point on the temperature axis represents dry air.
The curved lines between the saturation line and the temperature axis
marked in even per cents represent mixtures of air and water of
definite percentage humidities. (Simply the curved lines below the line
for saturated air represent various per cent humidities). Using equation
4 (following equation) linear interpolation between the saturation line
and the temperature axis may be used to locate the lines of constant
percentage humidity.
The slanting lines running upward and to the left of the saturation line
are called adiabatic saturation cooling lines. They are plots of equation
10
--------------(10)
-------------(17)
Each line is drawn for a given constant value of adiabatic-saturation
temperature. For a given value of Ts, both Hs and λs are fixed, and the
line of H versus T can be plotted by assigning values of H and
calculating corresponding values of T. Inspection of equation (17)
shows that the slope of an adiabatic cooling line, if drawn on truly
rectangular coordinates, is ─Cs/λs, and this slop depends on the
humidity by the equation (8) given as:
On rectangular coordinates, then, the adiabatic-cooling lines are
neither straight nor parallel. In the figure the humidity coordinates
have been distorted in such a manner that the adiabatic cooling lines
are straight and parallel so that interpolation between them is easy.
The left-hand ends of the adiabatic cooling lines are indentified with
the corresponding adiabatic-saturation temperatures.
Lines are shown on the figure for the specific volume of dry air and the
saturated volume. Both lines are plots of volume against temperature.
Volumes are read on the scale at the left. Coordinates of points on
these lines are calculated by the use of equation (a). Linear
interpolation between the two lines, based on percentage humidity,
gives the humid volume of unsaturated air.
Also, the relation between the humid heat Cs and humidity is shown as
a line on the figure. This line is a plot of equation (8) as given below:
The scale for Cs is at the top of the chart.
Use of humidity chart
The utility of the humidity chart as a source of data on a definite air-
water mixture may be shown by reference to figure. Assume for
example that a given stream of undersaturated air is known to have a
temperature T1 and a percentage humidity HA1. Point a represents this
air on the chart. This point is the intersection of the constanttemperature line for T1 and the constant-percentage-humidity line for
HA1. The humidity H1 of the air is given by point b, the humidity
coordinate of point a.
The dew point is found by following the constant-humidity line
through point a to the left to point c on the 100 per cent line.
The dew point is then read at point d on the temperature axis.
Adiabatic-saturation temperature is the temperature applying to the
adiabatic-cooling line through point a. The humidity at adiabatic
saturation is found by following the adiabatic line through point a to its
intersection e on the 100 per cent line, and reading humidity Hs at
point f on the humidity scale. Adiabatic saturation temperature Ts is
given by point g. If the original air is subsequently saturated at
constant temperature, the humidity after saturation is found by
following the constant-temperature line through point a to point h on
the 100 per cent line, and reading the humidity at point j.
The humid volume of the original air is found by locating points k and
l on the curves for saturated and dry volumes, respectively,
corresponding to temperature T1.
Problem 2:
The temperature and dew point of the air entering a certain dryer are
150 and 600F, respectively. What additional data for this air can be
read from the humidity chart?
Solution: The dew point is the temperature coordinate on the
saturation line corresponding to the humidity of the air. The saturation
humidity for a temperature of 600F is 0.011 lb of water per pound of
dry air, and this is the humidity of the air. From the temperature and
humidity of the air, the point on the chart for this air located.
At H=0.011 and T=1500F, the percentage humidity HA is found by
interpolation to be 5.9. The adiabatic-cooling line through this point
intersects the 100 per cent line at 850F, and this is the adiabatic-
saturation temperature. The humidity of saturated air at this
temperature is 0.026 Ib of water per pound of dry air. The humid heat
of the air is 0.245 Btu/(Ib dry air)(0F). The saturated volume at 1500F
is 20.7 ft3 per pound of dry air, and the specific volume of dry air at
1500F is 15.35 ft3/Ib. The humid volume is, then
vH = 15.35 + 0.059 (20.7 ─15.35) = 15.67 ft3/Ib dry air
Determination of humidity
If the wet-bulb and dry-bulb temperatures are known, the humidity
may be determined by the methods described.
Psychrometric method
A more common method for determining the humidity of air is to
determine simultaneously the wet-bulb and the dry bulb temperatures.
This is done by rapidly passing a stream of air over two thermometers,
the bulb of one of which is dry. The bulb of the other is kept wet by
means of a cloth sack either dipped in water or supplied with water.
The sling psychrometer is regularly used in meteorological
determinations. In this the two thermometers are fastened in a metal
frame that may be whirled about a handle.
The psychrometer is whirled for some seconds (rotation enhances
evaporative cooling ) and the reading of the wet-bulb thermometer is
observed as quickly as possible. The operation is repeated until
successive readings of the wet-bulb thermometer show that it has
reached its minimum temperature. This locates point ‘e’ in the figure.
By drawing an adiabatic line through point ‘e’, the intersection of this
adiabatic line with the temperature Ti fixes the point ‘a’, and
therefore, determines the humidity H1.
Cooling Towers
The same operation that is used to humidify air may also be used to
cool water.
Warm water is discharged from condensers or other apparatus
Value of this water is such that it is more economical to cool it and
reuse it than to discard it
The cooling is accomplished by bringing the water into contact with
unsaturated air under such conditions that the air is humidified and the
water brought approximately to the wet-bulb temperature. The method
is applicable only in those cases where the wet-bulb temperature of the
air is below the desired temperature of the exit water.
The water vapor produced by the evaporation of water in the cooling
tower is carried away by the air circulating through the tower. Thus the
air coming out of the cooling tower will be warm and quite humid.
The amount of water that can evaporate will naturally depend upon the
capability of the circulating air to take in moisture or water vapor. The
wet-bulb depression of air (i.e., the difference between the dry and wet
bulb temperatures of the air) is the determining factor for the amount
of water vapor that the air can take. For example air at 350C dry-bulb
and 250C wet-bulb temperature can take more water vapor than air at
350C dry and 300C wet-bulb temperature. Thus it is the wet-bulb
temperature of air around the cooling tower, which determines the
amount of water that can evaporate in the tower.
From above, it is clear that water cannot be cooled to below the wet-
bulb temperature. In practice the discharge temperature of the water
must differ from the wet-bulb temperature by at least 4 or 50F. This
difference in temperature is known as the approach. The change in
temperature in the water from inlet to outlet is known as the range.
Thus if water were cooled from 95 to 800F by exposure to air with a
wet-bulb temperature of 700F, the range would be 150F and the
approach 100F.
The lowest temperature to which water may be cooled throughout the
year depends not on the summer dry-bulb temperature but on the
maximum wet-bulb temperature. Tables of maximum wet-bulb
temperatures have been published for various points in the USA and
many parts of the world.
The loss of water by evaporation during cooling is small. Since
roughly 1000 Btu is required to vaporize 1 Ib of water, 100 Ib must be
cooled 100F (range) in the water temperature there is an evaporation
loss of 1 per cent.
In addition there are mechanical spray losses, but in well-designed
tower these amount to only about 0.2 per cent.
Under the conditions given above, then, the total loss of water during
passage through the cooler would be approximately 15 (range)/10 × 1
+ 0.2 = 1.7
There are three (03) types of apparatus in which cooling may be
accomplished:
Spray ponds
Natural-draft cooling towers
Mechanical-draft cooling towers
Spray ponds: All methods for cooling water by bringing it into contact
with air involve subdividing the water so as to present the largest
possible surface to the air. This may be accomplished most simply by
merely spraying the water from a spray nozzle. The sprays must
obviously be placed over a basin to catch the water, and consequently
such an arrangement is usually known as a spray pond.
In these devices water is cooled by spraying it upward into the air and
allowing it to fall back into a shallow pond. Spray nozzles set about 2
feet above the pond are arranged so that the spray pattern from one
nozzle does not overlap that from any other. Otherwise the humid air
would not readily escape. The pond is about 3 ft deep and often very
large in area. Since there is only a single dispersion of water and no
positive circulation of the air, the cooling capacity of even a sizable
pond is limited. Such ponds are convenient for small capacities or
where ground is not expensive. The power for pumping the water is
appreciable, since the production of a satisfactory spray requires a
certain minimum nozzle pressure.
Natural-draft cooling towers
Atmospheric circulation type: The circulation of air through the tower
is essentially across it in a horizontal direction rather than up through it
in a vertical direction.
Wind velocities alone are depended on for moving the air through the
tower.
The water is distributed by allowing it to fall over baffles of varies
types. This consists of flat boards 1 by 6 in. in cross section, laid with
small gaps between the boards. All the boards in any on layer run in
the same direction. Water is distributed over the tower by means of a
more or less complicated systems of troughs, and louvers are provided
along the sides to prevent excessive amounts of water being carried
Natural-draft cooling tower
away as sprays by the wind.
These towers may be 20 to 50 ft high, 8 to16 ft wide (in the direction
of the prevailing wind), and the length is dependent on the amount of
water cooled.
The principal difficulties in the operation of such a tower are to secure
complete distribution of water over the lower surfaces and to prevent
as far as possible losses of water by wind. Some recent designs of drift
eliminators are claimed to be superior to the louvers.
Chimney-type natural-draft tower
This tower depends on the fact that the air is warmed by the water and
therefore may produce an upward draft.
The sides of such a tower are completely enclosed all the way to the
top except for air inlets near the bottom.
The grid material, which distributes the water, is confined to a
relatively short section in the lower part of the tower, and most of the
structure is necessary for producing the draft.
The resistance to the flow of air must be kept at a minimum, and
therefore the filling zigzag slats are used.
The disadvantages of the chimney type of tower are the height which is
necessary to produce the draft and the fact that the water must be
hotter than the dry-bulb temperature of the air in order to warm the air
and produce a draft.
Natural-draft chimney
cooling tower
type
Mechanical-draft cooling towers
In most mechanical-draft cooling towers air is drawn through the
filling by large fans set at the top of the unit as shown in the figure.
Such towers are known as “induced-draft towers”.
The older “forced-draft towers’’, in which air is blown through the
filling by a fan at the bottom of the tower. Induced-draft towers are
preferred because they avoid return of saturated air back into the tower
and this does happen with forced draft.
In induced-draft towers of medium size, cooling from 1000 to 5000
gal/min water, the air enters through the side of the tower near the
bottom, flows upward through the filling, and passes between zigzag,
or drift eliminators, to the fan intake.
In large towers, cooling from 5000 to 100000 gal/min of water, cross
flow of the air is used.
A central fan draws air inward and upward through two sets of filling
(packing), one on each side, past inclined drift eliminators. The entire
side of the tower is left open for intake of air.
Basic components of cooling tower
Frame and casing. Most towers have structural frames that support the
exterior enclosures (casings), motors, fans, and other components. Early
cooling towers were constructed with wooden structural frames. The use
of wood preservatives has significant undesirable environmental side
effects. Cooling tower needs fire protection. Wood is highly combustible
and fires in cooling towers that are out of service have been a relatively
common occurrence. To reduce the effects of corrosion in a wet tower
environment
galvanized steel and stainless steels are used. Other
materials: Concrete, glass fiber structural tower frames.
Cooling tower (induced draft cross flow type)
Fill. The function of the tower fill is to provide a large “contact area”
between the water flow and the airflow to promote evaporation and heat
transfer. There are two types of fill:
Splash fill: Splash fill was introduced in 1940 to improve the cooling
tower efficiency. Since most cooling towers of that era were constructed
of wood, splash fill was fabricated from wooden slats that were then
stacked in the tower air plenum to create a cascading path for the water
as it fell by gravity through the tower.
Fill slats were either flat or triangular shaped, which tended to reduce the
air flow pressure drop. Modern splash fill is typically constructed of
PVC slats or V-shaped bars that are designed to provide good droplet
formation and eliminate the rot problem common to wood
Splash fill
in wet environments. Ceramic fill is an alternative splash fill material
sometimes used in HVAC applications.
Film fill: Introduced in 1960 and created a new concept in cooling tower
design. Instead of breaking the water flow into fine droplets, film fill
provides large surface areas over which the water flows. With the large
areas and slower falling speeds than in splash fill, water forms a thin
sheet or film as it flows across the fill surfaces, creating large air-water
contact area and efficient evaporative heat transfer.
Film fill is typically constructed of thin sheets of PVC, stacked in
vertical layers and formed with corrugations to ensure even water
distribution over the entire fill surface. This configuration has low
resistance to airflow; the air pressure drop through the tower is low.
Casing. A cooling tower’s casing performs two roles.
First, it forms an enclosure around the fill to create a contained air path
or plenum, forcing the air flow through the fill.
Second, it simply helps to keep the water inside the tower. Galvanized
steel-framed cooling towers are typically encased by galvanized steel,
fiber glass, UV-inhibited plastic panels.
Stainless-steel and fiberglass-framed cooling towers are normally
encased by stainless-steel, fiberglass, UV-inhibited plastic panels.
Cold-water basin. This is a concrete reinforced structure designed to
store water and provide a foundation upon which the rest of the cooling
tower can be supported. The basin is designed to collect the water as it
flows across the horizontal fill and downward. The water basin provides
suction for the water pump and must be able to resist chemical attack.
Drift-eliminators: As air flows through the tower, particularly when the
tower fans are operating on high speed, some of the recirculating water
becomes entrained (To carry suspended particles into the vapor phase) as
droplets in the air flow and is carried off. This is called drift, this water
loss contributes nothing to the efficiency of the tower while increasing
makeup water and water treatment chemical requirements.
To reduce the amount of drift released from a tower, manufacturer
place an assembly, called a drift eliminator in the airstream to remove
the entrained water droplets. The devices force the air to make a three
or four high-velocity directional changes (about 900). Water droplets,
then, will impinge on the eliminators and drain back into the fill.
Wet decks/Water distributor
The wet deck is located at the top of the tower and its job is to
distribute the incoming warm condenser water as evenly as possible
over the fill to ensure uniform heat transfer.
Louvers: Louvers are inclined blade or passage type assemblies fitted
at the air inlet wall of a cooling tower to promote uniform air entry
into the tower while preventing water splashout. Crossflow towers are
always provided with louvers to allow uniform air flow all along the
wall. Closely spaced and steeply sloped louvers are very effective for
water contaminant. The most important louver materials
corrugated fire-retardant fiber-reinforced polyester
treated wood
asbestos cement (not in use)
Equipment
for
dehumidifiers
humidification
operations:
Humidifiers
and
The evaporation of water into air for the purpose of increasing the air
humidity is known as humidification.
The evaporation of water into air can also be used for the purpose of
cooling the water.
Dehumidification consists of condensing water from air to decrease the
air humidity. All these processes are of considerable industrial
importance and involve the contacting of air and water accompanied by
heat and mass transfer.
Theory and Calculation of Air-Water Process
The mechanism of the reaction of unsaturated air and water at the wet bulb
temperature of the air is controlled by the flow of heat and the diffusion of
water vapor through the air at the interface between the air and the water.
In case of an adiabatic cooling line:
Liquid remains at a constant adiabatic-saturation temperature.
No temperature gradient through the liquid since there is no flow of
sensible heat into or from the liquid phase.
In dehumidification and in cooling:
The temperature of the liquid is changing.
Sensible heat flows into or from the liquid and a temperature gradient is
set up.
This introduces a liquid-film resistance to the flow of heat in the
liquid phase. But it is apparent that there can be no liquid-phase mass
transfer resistance in any of these cases, since there can be no
concentration difference in pure water.
The relationships of the transfer of heat and of vapor in all situations of
gas-liquid contact can be shown in the figures 1, 2, 4 and 5.
Distances measured perpendicular to the interface are plotted as
abscissas, and temperatures and humidities as ordinates.
In all figures let
Tx = temperature of bulk of liquid
Ti = temperature at interface
Ty = temperature of bulk of gas
Hi = humidity at interface
H = humidity of bulk of gas
Broken lines represent diffusion of the vapor through the gas phase
Solid lines represent flow of heat both latent and sensible through gas
and liquid phases
Ti and Hi represent equilibrium conditions and therefore are
coordinates of points lying on the saturation line on the humidity
chart.
Adiabatic humidification with liquid at constant temperature is shown
diagrammatically in Figure 1.
The latent heat flow from liquid to gas just balances the sensible heat
flow from gas to liquid
Figure 1: Conditions in adiabatic humidifier
There is no temperature gradient in the liquid.
The gas temperature Ty must be higher than the interface temperature
Ti in order that sensible heat may flow to the interface
Hi must be greater than H in order that the gas be humidified
Conditions at one point in a dehumidifier are shown in the Figure 2.
•Here H is greater than Hi, and therefore vapor must diffuse to the
interface.
•Since Ti and Hi represent saturated air, Ty must be greater than Ti.
Vapor can be removed from unsaturated gas by direct contact with
sufficiently cold liquid without first bringing the bulk of the gas to
saturation.
Figure 2: Conditions in dehumidifier
oAs a result of the humidity and temperature gradients, the interface
receives both sensible heat and water vapor from the air.
oThe condensation of the water liberates latent heat, and both sensible
and latent heat are transferred to the water phase because of a
temperature difference Ti and Tx through the water.
The conditions in a countercurrent cooling tower depend on whether
the temperature of the water is above the dry-bulb temperature of the
air or between the dry-bulb and wet-bulb temperatures of the air.
In the first case (temperature of water above the dry bulb temperature
of the air or temperature of the air below the interface temperature) , as
for example, in the upper part of the cooling tower, the conditions are
shown diagrammatically in the Figure 3.
The water is being cooled both by evaporation (transfer of latent
heat) and by transfer of sensible heat
The humidity and temperature gradients of the air film decrease in
the direction of interface to air,
The temperature gradient (drop) tx─ti through the water must result
in a heat-transfer rate high enough to account for both of these heat
items (latent and sensible).
Figure 3: Conditions in top of cooling tower
In the lower part of the cooling tower, where the temperature of the
water is higher than that of the wet-bulb temperature of the air but may
be below the dry-bulb temperature, the conditions shown in the Figure
4 prevail.
 In this case the water is being cooled; hence the interface must be
cooled than the bulk of the water, and the temperature gradient through
the water is toward the interface (Ti is less than Tx).
 Since the air is being humidified adiabatically, there must be a flow
of sensible heat from the bulk of the air to the interface (Ty is greater
than Ti).
 Sum of the heat flowing from the bulk of the water to the interface
and from the bulk of the air to the interface results in evaporation at
Figure 4: Conditions in bottom of cooling tower
interface, and the resulting water vapor diffuses into the air (Hi is
greater than H).
 This flow of water vapor carries away from the interface as latent
heat all the heat supplied to the interface from both sides as sensible
heat.
 The resulting temperature gradient, Tx ─ Ti─ Ty, has a striking V
shape, as shown in the Figure 4.
Equations for Air-Water contacts
(Cooling tower)
Consider the countercurrent air-water contactor shown in the Figure.
The air at humidity Hb and temperature tyb enters the bottom of the
contactor and leaves at the top with a humidity Ha and temperature tya.
Water enters the top at temperature txa and leaves at the bottom at
temperature txb.
 The mass velocity of the gas is Ǵy Ib of dry air per square foot of
tower cross section per hour. The mass velocities of the water at inlet
and outlet are, respectively, Gxa and Gxb Ib per square foot of tower
cross section per hour.
Figure 6: Counter current gas-liquid contractor, flow diagram
Suppose that,
dZ = height of a small section of the tower at distance Z ft from the
bottom of the contact zone
Gx = mass velocity of water at height Z
ty = temperature of the gas at height Z
tx = temperature of water at height Z
H = humidity of the gas at height Z
ti = temperature at the interface
Hi = humidity at the interface
S = cross section of the tower, ft2
ZT = height of the contact section, ft
SdZ = small volume at the differential height dZ
The following equations may be written over the small volume SdZ
The enthalpy balance is:
Ǵy diy = d(Gx ix)---------------------(18)
Where iy and ix are the total enthalpies of air and water, respectively.
The rate of heat transfer from water to interface is
d(Gx ix) = hx (tx ─ ti) aH dZ ---------------------(19)
The rate of heat transfer from interface to air is
Ǵycs dty = hy (ti ─ ty) aH dZ ---------------------(20)
The rate of mass transfer of water vapor from interface to air is
Ǵy dH = ḱy (Hi ─ H) aM dZ ---------------------(21)
From equations 19-21
hx = heat transfer coefficient from water to interface
(liquid-phase heat transfer coefficient)
hy = heat transfer coefficient from interface to air
aH = heat transfer area in square feet per cubic foot of contact volume
(interfacial area for heat transfer per unit contact volume)
aM = mass transfer area in square feet per cubic foot of contact volume
(interfacial area for mass transfer per unit contact volume)
ḱy = mass transfer coefficient from interface to air
The factors aM and aH are not necessarily equal. If the contactor is
packed with solid packing, the water may not completely wet the
packing, and the area available for heat transfer, which is the entire
area of the packing, is larger than that for mass transfer, which is
limited to the surface that is actually wet.
Three rate equations 19, 20, 21 may be simplified and rearranged.
For the most cases, the rate of mass transfer of water vapor (amount of
water vaporized) from interface to air is small compared to the total
water feed. So neglecting the change of Gx with height, enthalpy of the
liquid may be written as:
ix = CL (tx ─ t0) --------------------------(22)
Where CL is the specific heat of the liquid (unity for water) and t0 is
the base temperature for computing enthalpy. Then equation 18
becomes:
d(Gx ix) = Gxdix = Gx CL dtx ------------------(23)
Substituting d(Gx ix) from equation (23) into equation (19)
d(Gx ix) = hx (tx ─ ti) aH dZ ---------------------(19)
Gx CL dtx= hx (tx ─ ti) aH dZ
This may be rearranged as follows:
-----------------------------(24)
Second, equation (20) may be rearranged to obtain
Ǵycs dty = hy (ti ─ ty) aH dZ ---------------------(20)
-----------------------------(25)
Third, equation (21) may be rearranged to obtain
Ǵy dH = ḱy (Hi ─ H) aM dZ ---------------------(21)
----------------------(26)
Finally, using equation 18, equation 23 may be written
----------------------(27)
Both sides of equation 21 are multiplied by λ0 and this resulting
equation is added to equation 20
Ǵy dH (λ0) + ǴyCs dty = λ0 [ḱy (Hi ─ H) aM dZ] + hy (ti ─ ty) aH dZ
=˃ Ǵy (Cs dty + λ0 dH) = [λ0 ḱy (Hi ─ H) aM + hy (ti ─ ty) aH] dZ
----------------------(28)
If the packing is completely wet with liquid, so that the area for mass
transfer equals that for heat transfer, aM = aH = a. Neglecting the
change of Cs with H, equation 9 gives on differentiation,
iy = Cs (ty ─t0) + Hλ0 (Eq. 9)
diy = Cs dty + λ0 dH
----------------------(29)
From equation 29 diy may be substituted in the left-hand side
of equation 28. This gives
Ǵy diy = [λ0 ḱy (Hi ─ H) a + hy (ti ─ ty) a] dZ
For the system air-water hy can be eliminated by using Lewis
relation as: hy = Cs ḱy
----------------------(30)
This gives
Ǵy diy = [λ0 ḱy (Hi ─ H) a + Cs ḱy(ti ─ ty) a] dZ
=˃ Ǵy diy = ḱy a [λ0 (Hi ─ H) + Cs (ti ─ ty)] dZ
=˃ Ǵy diy = ḱy a[λ0 Hi ─ λ0 H) + Cs ti ─ Cs ty] dZ
=˃ Ǵy diy = ḱy a [(λ0 Hi + Cs ti) ─ (λ0 H + Cs ty)] dZ
Equation 31 can be rewritten as
----------------------(31)
Ǵy diy = ḱy a[{λ0 Hi + Cs(ti ─t0)} ─ {λ0 H + Cs(ty ─t0)}] dZ
=˃ Ǵy diy = ḱy a[ii ─ iy] dZ
----------------------(32)
Because from equation 9: ii = Hiλ0 + Cs (ti ─t0) at interface
iy = Hλ0 + Cs (ty ─t0)
----------------------(32)
Second, from equations 18 & 19
Ǵy diy = hx (tx ─ ti) a dZ
----------------------(33)
Eliminating dZ from equations 32 & 33 and rearranging gives using
equation 30
------------(34)
Third, equation 25 is divided by equation 32, using the Lewis relation
giving:
[As hy = Cs ḱy]
------------(35)
Since the Lewis relation is used in their derivation, equations 32, 34 &
35 can be applied only to the air-water system and also for situations
where aM = aH.
Adiabatic Humidification
Adiabatic humidification corresponds to the process that the air leaving
the humidifier is not necessarily saturated (unlike adiabatic saturation),
and the design rate equations must be used to calculate the size of the
contact zone.
The inlet and outlet water temperature are equal
Makeup water enters at adiabatic-saturation temperature
 aM = aH = a
Wet-bulb and adiabatic saturation temperatures are equal and
constant. Therefore, txa = txb = ti = tx = ts = Constant
Where ts is the adiabatic-saturation temperature of the inlet air. Also for
water CL = 1.0. Equation 25
then becomes
------------(36)
------------(37)
Where VT = SZT is the total contact volume, in cubic feet, and
ṁ= ǴyS is the total mass rate of dry air, in pounds per hour.
An equivalent equation, based on mass transfer, may be derived from
equation 26, which is written for adiabatic humidification as
Since Hs, the saturation humidity at ts is constant, this equation may be
integrated in the same manner as equation 36 to give:
------------(38)
Problem 16 : (Final 2019)
The air supply for a dryer has a dry-bulb temperature of 700F and wetbulb temperature of 600F. If it is heated to 2000F by coils and blown
into the dryer. In the dryer it cools along the adiabatic cooling line and
leaves the dryer fully saturated. (1) what is dew-point of the initial air?
(2) what is its humidity? (3) what is its percent humidity? (4) how much
heat is needed to heat 100 cu.ft to 2000F? (5) how much water will be
evaporated per 100 cu.ft of entering air and (5) at what temperature
does the air leave the dryer?
Solution:
For initial air, adiabatic saturation temperature and wet-bulb
temperature may be considered the same.
Problem 15:
Air at 900F and 70% relative humidity is conditioned so that its final
state is 800F and 40% relative humidity. How much water was removed
from the air? Assuming that the barometer is at 14.7 psia. Vapor
pressures of water vapor at 900F and 800F are 0.6988 psia and 0.5073
psia respectively.
Solution:
The amount of water vapor removed (per pound of dry air) is the
difference between the humidity ratio (specific humidity) at the inlet
and the outlet of the conditioning unit. We will therefore evaluate
for both specified conditions.